如何在mathematica中求偏导数符号

Question

我希望Mathematica返回符号偏导数而不是实际导数。

StressMatrix = ( {
    {\[Sigma]11, \[Sigma]12, \[Sigma]13},
    {\[Sigma]21, \[Sigma]22, \[Sigma]23},
    {\[Sigma]31, \[Sigma]32, \[Sigma]33}
   } );
varList = ( {
   {\[Rho], \[Theta], z}
  } )
StressMatrix[[2, 3]]
varList[[1, 1]]
D[StressMatrix[[2, 3]], varList[[1, 1]]]

上面的代码返回零，但我希望它返回Sigma[2,3]相对于rho的符号偏导数。

我该怎么做呢？

Answer 1

您可以使用Inactivate，

Inactivate[D[StressMatrix[[2, 3]], varList[[1, 1]]]]

或Hold

Hold[D[StressMatrix[[2, 3]], varList[[1, 1]]]]

Answer 2

各种方法，包括指定的值(需要在保持后设置)。

Clear[σ23]

StressMatrix = Map[Hold,
   {{σ11, σ12, σ13}, {σ21, σ22, σ23}, {σ31, σ32, σ33}}, {2}];
varList = {{ρ, θ, z}};

σ23 = 4 ρ^2;

expr = StandardForm[
   "∂" <> StringTake[ToString[StressMatrix[[2, 3]]], {6, -2}]/
    "∂" <> ToString[varList[[1, 1]]]];

symbolic = Inactive[D][ReleaseHold@StressMatrix[[2, 3]], varList[[1, 1]]];

result = D[ReleaseHold@StressMatrix[[2, 3]], varList[[1, 1]]];

Row[{expr, " = ", symbolic, " = ", result}]

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另一个选择

symbolic2 = StringJoin["D[",
  StringTake[ToString[StressMatrix[[2, 3]]], {6, -2}], ",", 
  ToString@varList[[1, 1]], "]"];

Row[{expr, " = ", symbolic2, " = ", ToExpression[symbolic2]}]

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最后

Clear[σ23]

StressMatrix = 
  Map[HoldForm, {{σ11, σ12, σ13}, {σ21, σ22, σ23}, {σ31, σ32, σ33}}, {2}];
varList = {{ρ, θ, z}};

σ23 = 4 ρ^2;

expr = StandardForm[
   "∂" <> ToString[StressMatrix[[2, 3]]]/
    "∂" <> ToString[varList[[1, 1]]]];

symbolic = Inactive[D][ToString@StressMatrix[[2, 3]], varList[[1, 1]]];

result = D[ReleaseHold@StressMatrix[[2, 3]], varList[[1, 1]]];

Row[{expr, " = ", symbolic, " = ", result}]

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